\(\renewcommand{\hat}[1]{\widehat{#1}}\)

Shared Qs (015_linear)


  1. Question

    Below, a specific arithmetic sequence, with a first element equal 20 and common difference equal 9, is defined recursively, where \(n\) is any whole number larger than 1. \[a_{[1]} = 20\] \[d = 9\] \[a_{[n]} = a_{[n-1]}+d\] Using that definition we can find the first few terms. \[a_{[2]} ~=~ a_{[1]}+d ~=~ 20+9 ~=~ 29 \] \[a_{[3]} ~=~ a_{[2]}+d ~=~ 29+9 ~=~ 38 \] \[a_{[4]} ~=~ a_{[3]}+d ~=~ 38+9 ~=~ 47 \] \[a_{[5]} ~=~ a_{[4]}+d ~=~ 47+9 ~=~ 56 \]

    We say the first element is 20, the second element is 29, the third element is 38, the fourth element is 47, and the fifth element is 56.

    The index is the address, so \(a_{[2]}=29\) says that the term with an index of 2 has a value of 29.

    To find the value of an element with a large index, it is useful to know the explicit formula:

    \[a_{[n]} ~~=~~ a_{[1]}~+~(n-1)\cdot d \]

    Find \(a_{[68]}\): the value of the element with an index equaling 68.


    Solution


  2. Question

    Below, a specific arithmetic sequence, with a first element equal 30 and common difference equal 10, is defined recursively, where \(n\) is any whole number larger than 1. \[a_{[1]} = 30\] \[d = 10\] \[a_{[n]} = a_{[n-1]}+d\] Using that definition we can find the first few terms. \[a_{[2]} ~=~ a_{[1]}+d ~=~ 30+10 ~=~ 40 \] \[a_{[3]} ~=~ a_{[2]}+d ~=~ 40+10 ~=~ 50 \] \[a_{[4]} ~=~ a_{[3]}+d ~=~ 50+10 ~=~ 60 \] \[a_{[5]} ~=~ a_{[4]}+d ~=~ 60+10 ~=~ 70 \]

    We say the first element is 30, the second element is 40, the third element is 50, the fourth element is 60, and the fifth element is 70.

    The index is the address, so \(a_{[2]}=40\) says that the term with an index of 2 has a value of 40.

    To find the value of an element with a large index, it is useful to know the explicit formula:

    \[a_{[n]} ~~=~~ a_{[1]}~+~(n-1)\cdot d \]

    Find \(a_{[66]}\): the value of the element with an index equaling 66.


    Solution


  3. Question

    Below, a specific arithmetic sequence, with a first element equal 22 and common difference equal 3, is defined recursively, where \(n\) is any whole number larger than 1. \[a_{[1]} = 22\] \[d = 3\] \[a_{[n]} = a_{[n-1]}+d\] Using that definition we can find the first few terms. \[a_{[2]} ~=~ a_{[1]}+d ~=~ 22+3 ~=~ 25 \] \[a_{[3]} ~=~ a_{[2]}+d ~=~ 25+3 ~=~ 28 \] \[a_{[4]} ~=~ a_{[3]}+d ~=~ 28+3 ~=~ 31 \] \[a_{[5]} ~=~ a_{[4]}+d ~=~ 31+3 ~=~ 34 \]

    We say the first element is 22, the second element is 25, the third element is 28, the fourth element is 31, and the fifth element is 34.

    The index is the address, so \(a_{[2]}=25\) says that the term with an index of 2 has a value of 25.

    To find the value of an element with a large index, it is useful to know the explicit formula:

    \[a_{[n]} ~~=~~ a_{[1]}~+~(n-1)\cdot d \]

    Find \(a_{[41]}\): the value of the element with an index equaling 41.


    Solution


  4. Question

    Below, a specific arithmetic sequence, with a first element equal 11 and common difference equal 14, is defined recursively, where \(n\) is any whole number larger than 1. \[a_{[1]} = 11\] \[d = 14\] \[a_{[n]} = a_{[n-1]}+d\] Using that definition we can find the first few terms. \[a_{[2]} ~=~ a_{[1]}+d ~=~ 11+14 ~=~ 25 \] \[a_{[3]} ~=~ a_{[2]}+d ~=~ 25+14 ~=~ 39 \] \[a_{[4]} ~=~ a_{[3]}+d ~=~ 39+14 ~=~ 53 \] \[a_{[5]} ~=~ a_{[4]}+d ~=~ 53+14 ~=~ 67 \]

    We say the first element is 11, the second element is 25, the third element is 39, the fourth element is 53, and the fifth element is 67.

    The index is the address, so \(a_{[2]}=25\) says that the term with an index of 2 has a value of 25.

    To find the value of an element with a large index, it is useful to know the explicit formula:

    \[a_{[n]} ~~=~~ a_{[1]}~+~(n-1)\cdot d \]

    Find \(a_{[77]}\): the value of the element with an index equaling 77.


    Solution


  5. Question

    Below, a specific arithmetic sequence, with a first element equal 2 and common difference equal 7, is defined recursively, where \(n\) is any whole number larger than 1. \[a_{[1]} = 2\] \[d = 7\] \[a_{[n]} = a_{[n-1]}+d\] Using that definition we can find the first few terms. \[a_{[2]} ~=~ a_{[1]}+d ~=~ 2+7 ~=~ 9 \] \[a_{[3]} ~=~ a_{[2]}+d ~=~ 9+7 ~=~ 16 \] \[a_{[4]} ~=~ a_{[3]}+d ~=~ 16+7 ~=~ 23 \] \[a_{[5]} ~=~ a_{[4]}+d ~=~ 23+7 ~=~ 30 \]

    We say the first element is 2, the second element is 9, the third element is 16, the fourth element is 23, and the fifth element is 30.

    The index is the address, so \(a_{[2]}=9\) says that the term with an index of 2 has a value of 9.

    To find the value of an element with a large index, it is useful to know the explicit formula:

    \[a_{[n]} ~~=~~ a_{[1]}~+~(n-1)\cdot d \]

    Find \(a_{[47]}\): the value of the element with an index equaling 47.


    Solution


  6. Question

    Below, a specific arithmetic sequence, with a first element equal 20 and common difference equal 14, is defined recursively, where \(n\) is any whole number larger than 1. \[a_{[1]} = 20\] \[d = 14\] \[a_{[n]} = a_{[n-1]}+d\] Using that definition we can find the first few terms. \[a_{[2]} ~=~ a_{[1]}+d ~=~ 20+14 ~=~ 34 \] \[a_{[3]} ~=~ a_{[2]}+d ~=~ 34+14 ~=~ 48 \] \[a_{[4]} ~=~ a_{[3]}+d ~=~ 48+14 ~=~ 62 \] \[a_{[5]} ~=~ a_{[4]}+d ~=~ 62+14 ~=~ 76 \]

    We say the first element is 20, the second element is 34, the third element is 48, the fourth element is 62, and the fifth element is 76.

    The index is the address, so \(a_{[2]}=34\) says that the term with an index of 2 has a value of 34.

    To find the value of an element with a large index, it is useful to know the explicit formula:

    \[a_{[n]} ~~=~~ a_{[1]}~+~(n-1)\cdot d \]

    Find \(a_{[69]}\): the value of the element with an index equaling 69.


    Solution


  7. Question

    Below, a specific arithmetic sequence, with a first element equal 5 and common difference equal 9, is defined recursively, where \(n\) is any whole number larger than 1. \[a_{[1]} = 5\] \[d = 9\] \[a_{[n]} = a_{[n-1]}+d\] Using that definition we can find the first few terms. \[a_{[2]} ~=~ a_{[1]}+d ~=~ 5+9 ~=~ 14 \] \[a_{[3]} ~=~ a_{[2]}+d ~=~ 14+9 ~=~ 23 \] \[a_{[4]} ~=~ a_{[3]}+d ~=~ 23+9 ~=~ 32 \] \[a_{[5]} ~=~ a_{[4]}+d ~=~ 32+9 ~=~ 41 \]

    We say the first element is 5, the second element is 14, the third element is 23, the fourth element is 32, and the fifth element is 41.

    The index is the address, so \(a_{[2]}=14\) says that the term with an index of 2 has a value of 14.

    To find the value of an element with a large index, it is useful to know the explicit formula:

    \[a_{[n]} ~~=~~ a_{[1]}~+~(n-1)\cdot d \]

    Find \(a_{[51]}\): the value of the element with an index equaling 51.


    Solution


  8. Question

    Below, a specific arithmetic sequence, with a first element equal 33 and common difference equal 9, is defined recursively, where \(n\) is any whole number larger than 1. \[a_{[1]} = 33\] \[d = 9\] \[a_{[n]} = a_{[n-1]}+d\] Using that definition we can find the first few terms. \[a_{[2]} ~=~ a_{[1]}+d ~=~ 33+9 ~=~ 42 \] \[a_{[3]} ~=~ a_{[2]}+d ~=~ 42+9 ~=~ 51 \] \[a_{[4]} ~=~ a_{[3]}+d ~=~ 51+9 ~=~ 60 \] \[a_{[5]} ~=~ a_{[4]}+d ~=~ 60+9 ~=~ 69 \]

    We say the first element is 33, the second element is 42, the third element is 51, the fourth element is 60, and the fifth element is 69.

    The index is the address, so \(a_{[2]}=42\) says that the term with an index of 2 has a value of 42.

    To find the value of an element with a large index, it is useful to know the explicit formula:

    \[a_{[n]} ~~=~~ a_{[1]}~+~(n-1)\cdot d \]

    Find \(a_{[65]}\): the value of the element with an index equaling 65.


    Solution


  9. Question

    Below, a specific arithmetic sequence, with a first element equal 14 and common difference equal 3, is defined recursively, where \(n\) is any whole number larger than 1. \[a_{[1]} = 14\] \[d = 3\] \[a_{[n]} = a_{[n-1]}+d\] Using that definition we can find the first few terms. \[a_{[2]} ~=~ a_{[1]}+d ~=~ 14+3 ~=~ 17 \] \[a_{[3]} ~=~ a_{[2]}+d ~=~ 17+3 ~=~ 20 \] \[a_{[4]} ~=~ a_{[3]}+d ~=~ 20+3 ~=~ 23 \] \[a_{[5]} ~=~ a_{[4]}+d ~=~ 23+3 ~=~ 26 \]

    We say the first element is 14, the second element is 17, the third element is 20, the fourth element is 23, and the fifth element is 26.

    The index is the address, so \(a_{[2]}=17\) says that the term with an index of 2 has a value of 17.

    To find the value of an element with a large index, it is useful to know the explicit formula:

    \[a_{[n]} ~~=~~ a_{[1]}~+~(n-1)\cdot d \]

    Find \(a_{[77]}\): the value of the element with an index equaling 77.


    Solution


  10. Question

    Below, a specific arithmetic sequence, with a first element equal 17 and common difference equal 9, is defined recursively, where \(n\) is any whole number larger than 1. \[a_{[1]} = 17\] \[d = 9\] \[a_{[n]} = a_{[n-1]}+d\] Using that definition we can find the first few terms. \[a_{[2]} ~=~ a_{[1]}+d ~=~ 17+9 ~=~ 26 \] \[a_{[3]} ~=~ a_{[2]}+d ~=~ 26+9 ~=~ 35 \] \[a_{[4]} ~=~ a_{[3]}+d ~=~ 35+9 ~=~ 44 \] \[a_{[5]} ~=~ a_{[4]}+d ~=~ 44+9 ~=~ 53 \]

    We say the first element is 17, the second element is 26, the third element is 35, the fourth element is 44, and the fifth element is 53.

    The index is the address, so \(a_{[2]}=26\) says that the term with an index of 2 has a value of 26.

    To find the value of an element with a large index, it is useful to know the explicit formula:

    \[a_{[n]} ~~=~~ a_{[1]}~+~(n-1)\cdot d \]

    Find \(a_{[79]}\): the value of the element with an index equaling 79.


    Solution


  11. Question

    Below, a specific arithmetic sequence, with a first element equal 6 and common difference equal 13, is defined recursively, where \(n\) is any whole number larger than 1. \[a_{[1]} = 6\] \[a_{[n]} = a_{[n-1]}+13\]

    Find the index of the element with a value of 370. In other words, find \(i\) such that \(a_{[i]}=370\).


    Solution


  12. Question

    Below, a specific arithmetic sequence, with a first element equal 12 and common difference equal 13, is defined recursively, where \(n\) is any whole number larger than 1. \[a_{[1]} = 12\] \[a_{[n]} = a_{[n-1]}+13\]

    Find the index of the element with a value of 415. In other words, find \(i\) such that \(a_{[i]}=415\).


    Solution


  13. Question

    Below, a specific arithmetic sequence, with a first element equal 48 and common difference equal 12, is defined recursively, where \(n\) is any whole number larger than 1. \[a_{[1]} = 48\] \[a_{[n]} = a_{[n-1]}+12\]

    Find the index of the element with a value of 324. In other words, find \(i\) such that \(a_{[i]}=324\).


    Solution


  14. Question

    Below, a specific arithmetic sequence, with a first element equal 39 and common difference equal 5, is defined recursively, where \(n\) is any whole number larger than 1. \[a_{[1]} = 39\] \[a_{[n]} = a_{[n-1]}+5\]

    Find the index of the element with a value of 169. In other words, find \(i\) such that \(a_{[i]}=169\).


    Solution


  15. Question

    Below, a specific arithmetic sequence, with a first element equal 29 and common difference equal 4, is defined recursively, where \(n\) is any whole number larger than 1. \[a_{[1]} = 29\] \[a_{[n]} = a_{[n-1]}+4\]

    Find the index of the element with a value of 141. In other words, find \(i\) such that \(a_{[i]}=141\).


    Solution


  16. Question

    Below, a specific arithmetic sequence, with a first element equal 7 and common difference equal 10, is defined recursively, where \(n\) is any whole number larger than 1. \[a_{[1]} = 7\] \[a_{[n]} = a_{[n-1]}+10\]

    Find the index of the element with a value of 307. In other words, find \(i\) such that \(a_{[i]}=307\).


    Solution


  17. Question

    Below, a specific arithmetic sequence, with a first element equal 37 and common difference equal 3, is defined recursively, where \(n\) is any whole number larger than 1. \[a_{[1]} = 37\] \[a_{[n]} = a_{[n-1]}+3\]

    Find the index of the element with a value of 109. In other words, find \(i\) such that \(a_{[i]}=109\).


    Solution


  18. Question

    Below, a specific arithmetic sequence, with a first element equal 22 and common difference equal 4, is defined recursively, where \(n\) is any whole number larger than 1. \[a_{[1]} = 22\] \[a_{[n]} = a_{[n-1]}+4\]

    Find the index of the element with a value of 138. In other words, find \(i\) such that \(a_{[i]}=138\).


    Solution


  19. Question

    Below, a specific arithmetic sequence, with a first element equal 10 and common difference equal 11, is defined recursively, where \(n\) is any whole number larger than 1. \[a_{[1]} = 10\] \[a_{[n]} = a_{[n-1]}+11\]

    Find the index of the element with a value of 395. In other words, find \(i\) such that \(a_{[i]}=395\).


    Solution


  20. Question

    Below, a specific arithmetic sequence, with a first element equal 22 and common difference equal 12, is defined recursively, where \(n\) is any whole number larger than 1. \[a_{[1]} = 22\] \[a_{[n]} = a_{[n-1]}+12\]

    Find the index of the element with a value of 310. In other words, find \(i\) such that \(a_{[i]}=310\).


    Solution


  21. Question

    Let \(a_{i}\) represent the \(i\)th element of an arithmetic sequence, and \[a_{13} = 180\] \[a_{32} = 408\]

    Find the common difference.


    Solution


  22. Question

    Let \(a_{i}\) represent the \(i\)th element of an arithmetic sequence, and \[a_{30} = 433\] \[a_{48} = 685\]

    Find the common difference.


    Solution


  23. Question

    Let \(a_{i}\) represent the \(i\)th element of an arithmetic sequence, and \[a_{27} = 298\] \[a_{43} = 458\]

    Find the common difference.


    Solution


  24. Question

    Let \(a_{i}\) represent the \(i\)th element of an arithmetic sequence, and \[a_{19} = 123\] \[a_{34} = 198\]

    Find the common difference.


    Solution


  25. Question

    Let \(a_{i}\) represent the \(i\)th element of an arithmetic sequence, and \[a_{11} = 140\] \[a_{20} = 257\]

    Find the common difference.


    Solution


  26. Question

    Let \(a_{i}\) represent the \(i\)th element of an arithmetic sequence, and \[a_{35} = 268\] \[a_{53} = 394\]

    Find the common difference.


    Solution


  27. Question

    Let \(a_{i}\) represent the \(i\)th element of an arithmetic sequence, and \[a_{24} = 140\] \[a_{36} = 188\]

    Find the common difference.


    Solution


  28. Question

    Let \(a_{i}\) represent the \(i\)th element of an arithmetic sequence, and \[a_{40} = 531\] \[a_{50} = 661\]

    Find the common difference.


    Solution


  29. Question

    Let \(a_{i}\) represent the \(i\)th element of an arithmetic sequence, and \[a_{14} = 83\] \[a_{33} = 178\]

    Find the common difference.


    Solution


  30. Question

    Let \(a_{i}\) represent the \(i\)th element of an arithmetic sequence, and \[a_{32} = 514\] \[a_{40} = 634\]

    Find the common difference.


    Solution


  31. Question

    Let \(a_{i}\) represent the \(i\)th term of an arithmetic series, and \[a_1=9\] \[a_2=15\]

    Find the sum of the first 16 terms. In other words, \[\sum_{i=1}^{16}a_i = \,?\]


    Solution


  32. Question

    Let \(a_{i}\) represent the \(i\)th term of an arithmetic series, and \[a_1=11\] \[a_2=13\]

    Find the sum of the first 39 terms. In other words, \[\sum_{i=1}^{39}a_i = \,?\]


    Solution


  33. Question

    Let \(a_{i}\) represent the \(i\)th term of an arithmetic series, and \[a_1=20\] \[a_2=24\]

    Find the sum of the first 35 terms. In other words, \[\sum_{i=1}^{35}a_i = \,?\]


    Solution


  34. Question

    Let \(a_{i}\) represent the \(i\)th term of an arithmetic series, and \[a_1=12\] \[a_2=15\]

    Find the sum of the first 15 terms. In other words, \[\sum_{i=1}^{15}a_i = \,?\]


    Solution


  35. Question

    Let \(a_{i}\) represent the \(i\)th term of an arithmetic series, and \[a_1=6\] \[a_2=9\]

    Find the sum of the first 17 terms. In other words, \[\sum_{i=1}^{17}a_i = \,?\]


    Solution


  36. Question

    Let \(a_{i}\) represent the \(i\)th term of an arithmetic series, and \[a_1=15\] \[a_2=21\]

    Find the sum of the first 32 terms. In other words, \[\sum_{i=1}^{32}a_i = \,?\]


    Solution


  37. Question

    Let \(a_{i}\) represent the \(i\)th term of an arithmetic series, and \[a_1=17\] \[a_2=19\]

    Find the sum of the first 16 terms. In other words, \[\sum_{i=1}^{16}a_i = \,?\]


    Solution


  38. Question

    Let \(a_{i}\) represent the \(i\)th term of an arithmetic series, and \[a_1=13\] \[a_2=15\]

    Find the sum of the first 40 terms. In other words, \[\sum_{i=1}^{40}a_i = \,?\]


    Solution


  39. Question

    Let \(a_{i}\) represent the \(i\)th term of an arithmetic series, and \[a_1=17\] \[a_2=20\]

    Find the sum of the first 15 terms. In other words, \[\sum_{i=1}^{15}a_i = \,?\]


    Solution


  40. Question

    Let \(a_{i}\) represent the \(i\)th term of an arithmetic series, and \[a_1=4\] \[a_2=10\]

    Find the sum of the first 15 terms. In other words, \[\sum_{i=1}^{15}a_i = \,?\]


    Solution


  41. Question

    x y
    49.4 486.7
    53.7 539.6
    52.0 551.3
    57.6 602.5
    57.0 595.0
    48.8 519.4
    51.5 519.0
    58.8 585.1

    Find the trendline using a simple linear regression. Do not assume the \(y\)-intercept is 0.

    Using the linear model, predict \(y\) when \(x=51\).


    Solution


  42. Question

    x y
    85.3 646.5
    89.7 732.7
    78.5 597.1
    91.4 702.4
    90.3 715.2
    76.2 589.7
    80.7 649.5

    Find the trendline using a simple linear regression. Do not assume the \(y\)-intercept is 0.

    Using the linear model, predict \(y\) when \(x=71\).


    Solution


  43. Question

    x y
    26.4 92.5
    27.7 97.7
    22.3 79.6
    24.4 89.1
    26.2 91.9
    25.4 90.8
    29.3 98.9

    Find the trendline using a simple linear regression. Do not assume the \(y\)-intercept is 0.

    Using the linear model, predict \(y\) when \(x=13\).


    Solution


  44. Question

    x y
    25.6 140.8
    24.1 127.7
    22.4 115.8
    23.8 134.7
    22.0 122.0
    26.3 144.8
    24.2 124.0
    21.7 122.6

    Find the trendline using a simple linear regression. Do not assume the \(y\)-intercept is 0.

    Using the linear model, predict \(y\) when \(x=35\).


    Solution


  45. Question

    x y
    35.1 373.7
    34.9 365.5
    33.6 343.2
    42.0 429.4
    41.5 475.1
    31.5 333.3
    30.0 350.1
    29.1 316.2

    Find the trendline using a simple linear regression. Do not assume the \(y\)-intercept is 0.

    Using the linear model, predict \(y\) when \(x=36\).


    Solution


  46. Question

    x y
    36.3 210.2
    29.2 199.6
    36.8 240.0
    27.9 189.6
    35.7 236.2
    35.1 212.2
    35.0 213.0
    28.9 188.4

    Find the trendline using a simple linear regression. Do not assume the \(y\)-intercept is 0.

    Using the linear model, predict \(y\) when \(x=42\).


    Solution


  47. Question

    x y
    60.0 367.4
    59.0 373.8
    57.9 356.4
    62.9 381.2
    56.9 364.5
    58.7 359.5

    Find the trendline using a simple linear regression. Do not assume the \(y\)-intercept is 0.

    Using the linear model, predict \(y\) when \(x=47\).


    Solution


  48. Question

    x y
    16.2 111.9
    21.1 134.7
    13.2 79.0
    14.4 83.4
    13.2 86.2
    21.2 126.7
    19.3 124.6
    20.6 134.1
    23.7 131.8

    Find the trendline using a simple linear regression. Do not assume the \(y\)-intercept is 0.

    Using the linear model, predict \(y\) when \(x=3\).


    Solution


  49. Question

    x y
    40.7 297.6
    42.4 311.8
    42.3 306.7
    39.7 296.9
    41.2 307.7
    43.2 310.6
    44.2 326.6
    44.2 319.5

    Find the trendline using a simple linear regression. Do not assume the \(y\)-intercept is 0.

    Using the linear model, predict \(y\) when \(x=36\).


    Solution


  50. Question

    x y
    24.4 162.0
    24.2 158.8
    22.5 142.9
    21.7 144.2
    23.8 157.5
    22.5 141.2
    27.2 175.7
    26.9 172.0
    24.3 158.9

    Find the trendline using a simple linear regression. Do not assume the \(y\)-intercept is 0.

    Using the linear model, predict \(y\) when \(x=23\).


    Solution


  51. Question

    Solve the system: \[y = 8 x + 4\] \[y = 3 x - 1\]

    Your answers:



    Solution


  52. Question

    Solve the system: \[y = - 3 x - 3\] \[y = - 2 x - 1\]

    Your answers:



    Solution


  53. Question

    Solve the system: \[y = - 2 x - 7\] \[y = - \frac{x}{2} - 4\]

    Your answers:



    Solution


  54. Question

    Solve the system: \[y = 7 - 7 x\] \[y = - \frac{5 x}{2} - 2\]

    Your answers:



    Solution


  55. Question

    Solve the system: \[y = \frac{4 x}{5} - 7\] \[y = 7 - 2 x\]

    Your answers:



    Solution


  56. Question

    Solve the system: \[y = \frac{x}{3} + 4\] \[y = 8 - x\]

    Your answers:



    Solution


  57. Question

    Solve the system: \[y = 2 x + 2\] \[y = x + 4\]

    Your answers:



    Solution


  58. Question

    Solve the system: \[y = \frac{7 x}{4} - 6\] \[y = 3 - \frac{x}{2}\]

    Your answers:



    Solution


  59. Question

    Solve the system: \[y = \frac{x}{2} - 8\] \[y = 7 x + 5\]

    Your answers:



    Solution


  60. Question

    Solve the system: \[y = x - 2\] \[y = - x - 6\]

    Your answers:



    Solution


  61. Question

    Solve the system: \[4 x - 3 y = 12\] \[x - y = 2\]

    Your answers:



    Solution


  62. Question

    Solve the system: \[- 3 x + y = 6\] \[- x + y = 8\]

    Your answers:



    Solution


  63. Question

    Solve the system: \[x + 3 y = 3\] \[- 2 x + 3 y = 12\]

    Your answers:



    Solution


  64. Question

    Solve the system: \[x - y = 3\] \[- 7 x + 2 y = 14\]

    Your answers:



    Solution


  65. Question

    Solve the system: \[x - 3 y = 9\] \[2 x - 3 y = 12\]

    Your answers:



    Solution


  66. Question

    Solve the system: \[x - 2 y = 4\] \[- 5 x + 3 y = 15\]

    Your answers:



    Solution


  67. Question

    Solve the system: \[- 3 x - 2 y = 6\] \[3 x + y = 3\]

    Your answers:



    Solution


  68. Question

    Solve the system: \[x - y = 1\] \[2 x - 3 y = 6\]

    Your answers:



    Solution


  69. Question

    Solve the system: \[- x - 2 y = 2\] \[3 x - 2 y = 18\]

    Your answers:



    Solution


  70. Question

    Solve the system: \[- x + y = 3\] \[- 4 x + 5 y = 20\]

    Your answers:



    Solution


  71. Question

    A thief is stealing xots and yivs. Each xot has a mass of 5 kilograms and a volume of 10 liters. Each yiv has a mass of 20 kilograms and a volume of 15 liters. The thief can carry a maximum mass of 100 kilograms and a maximum volume of 150 liters. The profit from each xot is $2.31 and the profit from each yiv is $4.8.

    For your convenience, those numbers are organized in the table below.

    attribute xot yiv capacity
    mass (kg) 5 20 100
    volume (L) 10 15 150
    profit ($) 2.31 4.80 \(\infty\)

    What is the maximum profit the thief can produce? (In dollars.)


    Solution


  72. Question

    A thief is stealing xots and yivs. Each xot has a mass of 4 kilograms and a volume of 7 liters. Each yiv has a mass of 16 kilograms and a volume of 14 liters. The thief can carry a maximum mass of 64 kilograms and a maximum volume of 98 liters. The profit from each xot is $1.98 and the profit from each yiv is $5.64.

    For your convenience, those numbers are organized in the table below.

    attribute xot yiv capacity
    mass (kg) 4 16 64
    volume (L) 7 14 98
    profit ($) 1.98 5.64 \(\infty\)

    What is the maximum profit the thief can produce? (In dollars.)


    Solution


  73. Question

    A thief is stealing xots and yivs. Each xot has a mass of 6 kilograms and a volume of 5 liters. Each yiv has a mass of 18 kilograms and a volume of 20 liters. The thief can carry a maximum mass of 108 kilograms and a maximum volume of 100 liters. The profit from each xot is $7.77 and the profit from each yiv is $8.81.

    For your convenience, those numbers are organized in the table below.

    attribute xot yiv capacity
    mass (kg) 6 18 108
    volume (L) 5 20 100
    profit ($) 7.77 8.81 \(\infty\)

    What is the maximum profit the thief can produce? (In dollars.)


    Solution


  74. Question

    A thief is stealing xots and yivs. Each xot has a mass of 16 kilograms and a volume of 6 liters. Each yiv has a mass of 8 kilograms and a volume of 18 liters. The thief can carry a maximum mass of 128 kilograms and a maximum volume of 108 liters. The profit from each xot is $7.51 and the profit from each yiv is $8.01.

    For your convenience, those numbers are organized in the table below.

    attribute xot yiv capacity
    mass (kg) 16 8 128
    volume (L) 6 18 108
    profit ($) 7.51 8.01 \(\infty\)

    What is the maximum profit the thief can produce? (In dollars.)


    Solution


  75. Question

    A thief is stealing xots and yivs. Each xot has a mass of 18 kilograms and a volume of 6 liters. Each yiv has a mass of 9 kilograms and a volume of 12 liters. The thief can carry a maximum mass of 162 kilograms and a maximum volume of 72 liters. The profit from each xot is $6.85 and the profit from each yiv is $8.26.

    For your convenience, those numbers are organized in the table below.

    attribute xot yiv capacity
    mass (kg) 18 9 162
    volume (L) 6 12 72
    profit ($) 6.85 8.26 \(\infty\)

    What is the maximum profit the thief can produce? (In dollars.)


    Solution


  76. Question

    A thief is stealing xots and yivs. Each xot has a mass of 4 kilograms and a volume of 18 liters. Each yiv has a mass of 20 kilograms and a volume of 6 liters. The thief can carry a maximum mass of 80 kilograms and a maximum volume of 108 liters. The profit from each xot is $3.54 and the profit from each yiv is $2.41.

    For your convenience, those numbers are organized in the table below.

    attribute xot yiv capacity
    mass (kg) 4 20 80
    volume (L) 18 6 108
    profit ($) 3.54 2.41 \(\infty\)

    What is the maximum profit the thief can produce? (In dollars.)


    Solution


  77. Question

    A thief is stealing xots and yivs. Each xot has a mass of 6 kilograms and a volume of 4 liters. Each yiv has a mass of 9 kilograms and a volume of 12 liters. The thief can carry a maximum mass of 54 kilograms and a maximum volume of 48 liters. The profit from each xot is $1.55 and the profit from each yiv is $3.07.

    For your convenience, those numbers are organized in the table below.

    attribute xot yiv capacity
    mass (kg) 6 9 54
    volume (L) 4 12 48
    profit ($) 1.55 3.07 \(\infty\)

    What is the maximum profit the thief can produce? (In dollars.)


    Solution


  78. Question

    A thief is stealing xots and yivs. Each xot has a mass of 16 kilograms and a volume of 12 liters. Each yiv has a mass of 10 kilograms and a volume of 15 liters. The thief can carry a maximum mass of 160 kilograms and a maximum volume of 180 liters. The profit from each xot is $8.95 and the profit from each yiv is $7.86.

    For your convenience, those numbers are organized in the table below.

    attribute xot yiv capacity
    mass (kg) 16 10 160
    volume (L) 12 15 180
    profit ($) 8.95 7.86 \(\infty\)

    What is the maximum profit the thief can produce? (In dollars.)


    Solution


  79. Question

    A thief is stealing xots and yivs. Each xot has a mass of 16 kilograms and a volume of 5 liters. Each yiv has a mass of 4 kilograms and a volume of 15 liters. The thief can carry a maximum mass of 64 kilograms and a maximum volume of 75 liters. The profit from each xot is $5.68 and the profit from each yiv is $7.5.

    For your convenience, those numbers are organized in the table below.

    attribute xot yiv capacity
    mass (kg) 16 4 64
    volume (L) 5 15 75
    profit ($) 5.68 7.50 \(\infty\)

    What is the maximum profit the thief can produce? (In dollars.)


    Solution


  80. Question

    A thief is stealing xots and yivs. Each xot has a mass of 4 kilograms and a volume of 15 liters. Each yiv has a mass of 16 kilograms and a volume of 5 liters. The thief can carry a maximum mass of 64 kilograms and a maximum volume of 75 liters. The profit from each xot is $7.97 and the profit from each yiv is $3.62.

    For your convenience, those numbers are organized in the table below.

    attribute xot yiv capacity
    mass (kg) 4 16 64
    volume (L) 15 5 75
    profit ($) 7.97 3.62 \(\infty\)

    What is the maximum profit the thief can produce? (In dollars.)


    Solution